Persistent Homology Guided Force-Directed Graph Layouts

Recent work shows that sampling algorithms can be an effective tool for graph visualization. This paper extends prior work by applying edge sampling algorithms to speed up the spring force calculation in force-directed graph layout algorithms. An experiment on 72 graphs finds that some sampling algorithms achieve comparable quality as no sampling. This result is confirmed with visualizations of the graph layout results. However, runtime improvements are small, especially for graphs with 10,000 vertices or fewer, indicating that the runtime savings might not be worth the risk to layout quality. Therefore, this paper suggests that accurate spring forces may be more important to force-directed graph layout algorithms than accurate electric forces. A copy of this paper plus the code and data to reproduce the results are available at https://osf.io/4ja29/

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Force-Directed Graph Layouts by Edge Sampling

2019 IEEE 9th Symposium on Large Data Analysis and Visualization (LDAV) ◽

10.1109/ldav48142.2019.8944364 ◽

2019 ◽

Cited By ~ 1

Author(s):

Robert Gove

Keyword(s):

Directed Graph ◽

Graph Layouts ◽

Edge Sampling

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Placing Arrows in Directed Graph Layouts: Algorithms and Experiments

Computer Graphics Forum ◽

10.1111/cgf.14440 ◽

2022 ◽

Author(s):

Carla Binucci ◽

Walter Didimo ◽

Michael Kaufmann ◽

Giuseppe Liotta ◽

Fabrizio Montecchiani

Keyword(s):

Directed Graph ◽

Graph Layouts

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Computing Persistent Homology of Directed Flag Complexes

Algorithms ◽

10.3390/a13010019 ◽

2020 ◽

Vol 13 (1) ◽

pp. 19

Author(s):

Daniel Lütgehetmann ◽

Dejan Govc ◽

Jason P. Smith ◽

Ran Levi

Keyword(s):

Performance Analysis ◽

Directed Graph ◽

Persistent Homology ◽

Undirected Graphs ◽

Flag Complex ◽

Data Collections ◽

Flag Complexes ◽

Compute Time

We present a new computing package Flagser, designed to construct the directed flag complex of a finite directed graph, and compute persistent homology for flexibly defined filtrations on the graph and the resulting complex. The persistent homology computation part of Flagser is based on the program Ripser by U. Bauer, but is optimised specifically for large computations. The construction of the directed flag complex is done in a way that allows easy parallelisation by arbitrarily many cores. Flagser also has the option of working with undirected graphs. For homology computations Flagser has an approximate option, which shortens compute time with remarkable accuracy. We demonstrate the power of Flagser by applying it to the construction of the directed flag complex of digital reconstructions of brain microcircuitry by the Blue Brain Project and several other examples. In some instances we perform computation of homology. For a more complete performance analysis, we also apply Flagser to some other data collections. In all cases the hardware used in the computation, the use of memory and the compute time are recorded.

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Computing Persistent Homology of Directed Flag Complexes

10.20944/preprints201911.0366.v1 ◽

2019 ◽

Author(s):

Daniel Luetgehetmann ◽

Dejan Govc ◽

Jason P. Smith ◽

Ran Levi

Keyword(s):

Performance Analysis ◽

Directed Graph ◽

Persistent Homology ◽

Undirected Graphs ◽

Flag Complex ◽

Data Collections ◽

Flag Complexes ◽

Compute Time

We present a new computing package Flagser, designed to construct the directed flag complex of a finite directed graph, and compute persistent homology for flexibly defined filtrations on the graph and the resulting complex. The persistent homology computation part of Flagser is based on the program Ripser [2], but is optimised specifically for large computations. The construction of the directed flag complex is done in a way that allows easy parallelisation by arbitrarily many cores. Flagser also has the option of working with undirected graphs. For homology computations Flagser has an Approximate option, which shortens compute time with remarkable accuracy. We demonstrate the power of Flagser by applying it to the construction of the directed flag complex of digital reconstructions of brain microcircuitry by the Blue Brain Project and several other examples. In some instances we perform computation of homology. For a more complete performance analysis, we also apply Flagser to some other data collections. In all cases the hardware used in the computation, the use of memory and the compute time are recorded.

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